A Government-backed study published earlier this year said more than one-in-10 pupils had been sent to tutors at some point, with families paying up to £60-an-hour.

Manchester Grammar, a £9,000-a-year boys' day school, said it was reforming its admissions to clampdown on the practice, suggesting some pupils were winning places despite lacking the ability to succeed.

Dr Ray said he had been "terribly concerned by the negative impact of entrance exams on the intellectual development of our pupils".

Under new plans, all pupils starting the school this September have been forced to undergo a day-long assessment, in which they are monitored by teachers in a series of normal classes to see how they respond to lessons. They also sit a more demanding entrance test. Pupils are then admitted using a combination of the two systems.

"What it does is level the playing field," said Dr Ray. "We are doing is putting tutors out of the game and looking to see how [pupils] respond to us. We wanted to ensure that they were not disadvantaged if they were not crammed by a tutor or a prep school."

Manchester Grammar, whose alumni include the mathematician Sir Michael Atiyah, former England cricket captain Michael Atherton and the actor Ben Kingsley, has already announced it would become the first leading independent school to opt wholesale out of GCSEs.

From September, it will offer the more traditional International GCSE is almost all subjects after claiming existing exams were "too easy" for the most able pupils.